Journal
IEEE TRANSACTIONS ON NEURAL NETWORKS AND LEARNING SYSTEMS
Volume 29, Issue 1, Pages 218-224Publisher
IEEE-INST ELECTRICAL ELECTRONICS ENGINEERS INC
DOI: 10.1109/TNNLS.2016.2608834
Keywords
l(2)-minimization; equivalence; least square regression; low rank representation (LRR); rank minimization
Categories
Funding
- A*STAR Industrial Robotics Programme-Distributed Sensing and Perception under SERC Grant [1225100002]
- National Natural Science Foundation of China [61432012, 61673283]
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A lot of works have shown that frobenius-norm-based representation (FNR) is competitive to sparse representation and nuclear-norm-based representation (NNR) in numerous tasks such as subspace clustering. Despite the success of FNR in experimental studies, less theoretical analysis is provided to understand its working mechanism. In this brief, we fill this gap by building the theoretical connections between FNR and NNR. More specially, we prove that: 1) when the dictionary can provide enough representative capacity, FNR is exactly NNR even though the data set contains the Gaussian noise, Laplacian noise, or sample-specified corruption and 2) otherwise, FNR and NNR are two solutions on the column space of the dictionary.
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